I have been reading the forum for a year by now, but I just registered now, because it is required if you want to write something.

I think that simulating Polywell is useful even when it uses approximations.
Someone have even started http://www.mare.ee/indrek/ephi/. See the bottom part of the page.

The first reason to write a simulation is promotion. Visualization of the behavior of the Polywell helps laymen like investors and politics to understand it. The effort of creating a good enough model is not huge. Is someone working with ephi ?

The second reason to write a simulation is the evaluation of design parameters like sizes, geometries, field strengths, etc. Building a WB-X takes months, even years, but a good simulator can evaluate thousands of options in that time. The armies don't do nuclear tests anymore, because they can do the tests using computers. Of course, they have calibrated the model by real bomb experiments. In the case of Polywell, to create a good simulator, you need to have a lot of experimental measurement data. I assume that the current project creates a lot of data. BTW, where do they use the fast speed camera.

I agree that creating a real life Polywell is the most urgent thing to do. If it works, accelerating the designs by software simulations can be considered. If WB8 does not work, then simulations could be the only affordable way to find out why not?

MSimon wrote:I'm reading the Feynman Physics lectures on electrostatics/magnetics and it is clear that such a computation is devilish hard for the reason that a particle's magnetic field is purely relative. If there is no relative motion between two particles there can be no magnetic field interaction between them. And even then the motion must be cross product and depends on relative velocity.

Can't we simplify it?

Electro-magnetic interactions are relative, so, the mutual influence of two static (to each other) charges can be seen as electric, or electric+magnetic, or purely magnetic, depending on the (external) frame of reference the observer chooses.

Are we sure that choosing only one frame of reference and calculating the E and B fields of individual charges in it, and then using those to compute the influence in the movement on other charges, is wrong?

MSimon wrote:I'm reading the Feynman Physics lectures on electrostatics/magnetics and it is clear that such a computation is devilish hard for the reason that a particle's magnetic field is purely relative. If there is no relative motion between two particles there can be no magnetic field interaction between them. And even then the motion must be cross product and depends on relative velocity.

Can't we simplify it?

Electro-magnetic interactions are relative, so, the mutual influence of two static (to each other) charges can be seen as electric, or electric+magnetic, or purely magnetic, depending on the (external) frame of reference the observer chooses.

Are we sure that choosing only one frame of reference and calculating the E and B fields of individual charges in it, and then using those to compute the influence in the movement on other charges, is wrong?

It is not the frame of reference that matters. It is the relative motion of the particles. The frame of reference does not change the relative motions.

Engineering is the art of making what you want from what you can get at a profit.

Ben,
This seems to be specifically about electro-magnetics, i.e. light, radar, etc. What we are more interested in is static electro-magnets (magneto-statics) and particle motion in magnetic fields. Different beasty, it seems.

MSimon wrote:It is not the frame of reference that matters. It is the relative motion of the particles.

Well, that depends on what you want to do. I was aiming to simplify calculations. Computing the relative influence of every pair of charges, and then translating them to a frame of reference attached to the device seems overburdening, that is, if we can calculate directly in that frame.

And that's what bothers me, because I'm not sure I understand the interactions well enough.

By the way, if the interaction of each couple of particles can be calculated with a fixed number of mathematical operations (and I think that's the case), then the problem of calculating the whereabouts of a cloud of N of them inside a polywell is of the order of complexity (in the CS sense):

O(N^2 * B * L * t)

where N is the number of charges, B the magnetic field strength, L the magrid side, and t the time lapse

That order of complexity means that (if I'm not wrong, something very probable) maybe we could calculate the evolution of a cloud of 10^5 to 10^7 charges inside a virtual WB-6 like machine without a Blue Gene supercomputer, or getting too old waiting. If we dont use electrons but macroscopic charges I think we could learn something, or at least enhance our undertanding of the inside dinamics.

You make good points. However, with the wiffle ball critical to operation I'm not sure your calculation simplifications will solve the problem.

With actual data rules of thumb simplifications would help considerably. Our current problem is lack of public data. In fact the experimenters might not have enough data yet. Thus the "we will know in two years" statement.

Engineering is the art of making what you want from what you can get at a profit.

I'm sure you're right, and that's why I'm not even aiming to solve the polywell problem, just seeking clues, and just for a very specific aspect of it. If we can get a grasp at the charges dinamics, next we could try fathom another aspect (the inside B and/or E fields shape for instance?).

Job, studies, and family means I dont have much time to spare to programming, so I dont know if I'm going to be able to do it before we have real data. I'd like to, it'd be nice to compare it with my calcs, even if the results show I am dead wrong (as is most probable).

Under "Field Selection" choosing Torroidal Solenoid was interesting. With the field strength turned up and the particles turned into a stream towards the top. Interestingly, the occasional particle in the centre hardly moves. Also interesting is that stream seemed better with less stray particles when the number of coils were reduced a bit.

Source code is supplied. I wonder how hard it would be to configure it as a Polywell. In fact the "Monopole Attempt" descriebed here http://www.falstad.com/vector3dm/directions.html sounds a bit like it. However looking at it run, I picture the squezing of the magnetic field of the Ploywell by the trapped electrons and it would seem that the magnetic field is not really static. So would magnetostatics really be suitable to simulate the Polywell?

In theory there is no difference between theory and practice, but in practice there is.

It has previously been mentioned that simulating the Polywell is problematic due to every particle seeing every other. Effectively an O(N^2) problem. This article possibly indicates a method to reduce this to O(N). However I don't know what the likely limitations are.

Abstract. We consider a problem in dynamically constrained Monte Carlo dynamics and show that this leads to the generation of long ranged effective interactions. This allows us to construct a local algorithm for the simulation of charged systems without ever having to evaluate pair potentials or solve the Poisson equation. We discuss a simple implementation of a charged lattice gas as well as more elaborate off-lattice versions of the algorithm. There are analogies between our formulation of electrostatics and the bosonic Hubbard model in the phase approximation. Cluster methods developed for this model further improve the effciency of the electrostatics algorithm.

Computer modeling of charged systems is demanding due to the range of the Coulomb interaction. The direct evaluation of the Coulomb sum for N particles requires computation of the separations rij between all pairs of particles, which implies O(N2) operations are needed per sweep or time step.

It is surprising that the Coulomb interaction poses such tremendous di±culty; after all the underlying Maxwell equations are local. The question then arises as to what part of Maxwell's equations gives rise to electrostatic interactions. Is it possible to generate e®ective Coulomb interactions in a manner better adapted to computer simulation?